The elastic foundation of a heavy machine in Figure Q19 consists of elastic springs connected in series and in parallel. Each of the springs has stiffness coefficient k = 10000 N-m-1. The machine is of mass m = 1164 kg and it is pulled by a distance 0.05 m from its equilibrium position and thereafter released from rest, such that simple harmonic oscillations occur. Determine the maximum acceleration of the machine. Provide only the numerical value (in m-s-2) to two decimal places and do not include the units in the answer box. m k

The elastic foundation of a heavy machine in Figure Q19 consists of elastic springs connected in series and in parallel. Each of the springs has stiffness coefficient k = 10000 N-m-1. The machine is of mass m = 1164 kg and it is pulled by a distance 0.05 m from its equilibrium position and thereafter released from rest, such that simple harmonic oscillations occur. Determine the maximum acceleration of the machine. Provide only the numerical value (in m-s-2) to two decimal places and do not include the units in the answer box. m k

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: 3) A one-degree-of-freedom system has an effective mass M-4-kg, an effective spring stiffness…

A: To find (a) The natural frequency ωn and critical damping ratio ζ (b) The response q as a function…

Q: For the given figure, assume that the cylinder rolls without slipping. Use your favorite method to…

Q: The figure shows a structure composed of a beam and a system of springs that supports a box weighing…

A: Given:To find:(a) Equation of motion of the system.(b) The frequency and natural period.

Q: mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with…

Q: (Uso Virtnal Work) Problem 7 In the system shown has mass m, length 1, and mass moment of inertia I…

A: The Answer is Below

Q: 8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium…

A: The mass is The damping coefficient is The extension of spring is The initial velocity is The…

Q: b. The semidefinite system shown in Figure 6 consists of a translating mass m=100 kg attached to a…

Q: Solve for the following: 1. Equation of motion x(t). Assume Initial conditions for displacement and…

A: Solution: Given Data: m=10kgk1=100 N/mk2=80 N/mk3=75 N/mk4=120…

Q: Solve a,b,c and for c when the two dampers are connected to rigid bar (not parallel or series)

A: DefinitionEquivalent damping constant:The equivalent damping constant is a quantity that indicates…

Q: The period Ta of damped linear oscillation for a certain 0.9 kg mass is 0.25 s. If the stiffness of…

Q: A cylinder of mass m and mass moment of inertia JO rolls without slipping on the ground and is…

A: The cylinder rolls without slipping in the ground.

Q: 2-23. A rigid bar AB is weightless and pivots at A as shown in the accompanying figure. Determine…

A: It is asked to generate differential equation of motion and then find the natural frequceny

Q: Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and…

A: The mass moment of inertia of the beam is The mass moment of inertia of the disk is,To find the…

Q: A uniform rigid bar of length L and mass m is pinned at one end and restrained by a spring as shown…

Q: A large industrial cooling system of mass 160 kg is supported by six springs arranged in parallel.…

Q: Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shown below. Write the…

A: The objective of the question is to derive the equation of motion for a system consisting of two…

Q: The values of a, C, and bare > and , respectively.

Q: Use modal analysis to calculate the response of the drive train system of Problem 4.44 given by the…

A: Given : To find : Modal analysis

Q: Two identical thin bars, each of mass m and length L, are welded together at a right angle as shown…

A: Solution: Given Data: Displacement, xB=bsinωtStiffness = kLength =L The Equation of Motion of the…

Q: A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal…

Q: 14. For the system shown to the right, the disk of mass m rolls without slip and z mcasures the…

A: Let the radius of disc be 'r'.displacement of spring 3k, x'=2rθdisplacement of spring k=displacement…

Q: QI Calculate the frequency of damped oscillation of the system shown in Figure () for the value m=…

Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

For the system shown below, the disc of mass M rolls without slip. Assume that the mass M = 11 kg, the damping constant C - 209 Ns/kg and the stiffnesses K, = 9,036 N/m, K2 = 4,855 N/m, the radius of the disc R = 0.4 m and the moment of inertia of the disc about its centre I = MR² What is the damping ratio of the free vibration of this system? www K2 K1 M *No Slip
Pls see the question in the attcahed image and solve using either Newton’s method or Lagrange Energy method .
Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? L/2 A Jo=m L² k L/2 Joz-m R² full 0₂ R U B C
Consider the mechanical system of this figure comprising two wheels of mass m, inertia j, andthree springs each of stiffness k. The wheels move on two fixed horizontal surfaces during thesystem's free vibrations. Derive the mathematical model of this mechanical system.
+ b 3. A tuning fork is an example of a "resonant system", that is, one that has a low damping ratio. A model of a (half) tuning fork is rod of mass m with air drag modeled as a damper connected approximately at its middle, and a torsional spring at the base of the cantilever. Assume the cantilever rotates back and forth about its pivot by a small angle o. Because other forces are much larger, you can reasonably neglect the effect of gravity in this model. The moment of inertia of a cantilevered beam pinned at one end is equal to ml2, where I is its length. (a) What is the natural frequency of this system if m= 0.1 kg and k = 2548 Nm/rad, and 1 = 0.1 m. Please give the value in rad/s and Hz. (b) Find an upper bound on the damping coefficient b that insures that the damping ratio of the tuning fork is no greater than = 0.01. (c) For this damping ratio, what is the damped natural frequency of the system? (d) For this damping ratio, what is the decay rate (the size of the exponent…
Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu
A factory machine with a mass of 320 kg vibrations up and down with frequency of 8 Hz. Amplitude of engine movement of 2 mm. Calculate the maximum acceleration of the machine, and what is the maximum Newtonian force obtained?
A body weighing 5kg is attached to a very light bar as depicted below. The set-up is free to rotate in the vertical plane about pin support O. The force applied at point C makes the bar oscillate(via small rotation) about the position of equilibrium illustrated below a. Derive the differential equation of motion for the steady state angular displacement (theta) of the bar
0.5m 1m The figure shows a slender rod with a mass of 6 kg. Attached to the rod is a spring of stiffness k = 250 N /m .A moveable point mass m1= 1 kg is position at a distance x from the pivot point. You can assume small angle oscillations from the equilibrium position shown in the figure.
Write the x, y and z equations that would be used to solve the tension in each cable if the bucket weighs 250 lb. Express the equations in Cartesian vector form. Do not solve the equations. B 6 ft 4 2 ft 3 ft 6 ft 6 ft D 3 ft RE 5 ft
Solve step by step in digital form
Problem (1): Derive the equation of motion of the system shown in Figure and find: • The natural frequency of vibration • The damping ratio • The free damped frequency of vibration If m= 10 kg, c = 50 N-s/m, k = 1000 N/m, L= 1 m 44 3k Uniform rigid bar, mass m 2 2